How to cover a brick floor in kitchen

We live in a rental duplex home on the first floor. The house was raised up and our unit was built out but they left the original floor in the kitchen which is real, exposed, uneven brick. It gives the place charm but now that we have a baby, we want a new floor. We asked if we could use floor leveling material to cover up the brick and the landlord said no, we can only put something temporary down.

We put down a thin layer of foam (that gray stuff) and a sheet of linoleum over it, adhering the linoelum with molding. The linoleum sheet is thin and is starting to tear so we need a plan B. Any ideas?

Should we replace the linoleum with a thicker sheet so it doesn't tear? Can we put a thin layer of plywood over the foam and then put linoleum over that? Is there anyway for us to put down some type of tile or interlocking floor with that uneven brick underneath?

With any project you must take into consideration how
long you plan on living at this location and how much will this project cost.

I do not have an Ideal solution but I would try the
plywood approach. To reduce movement, tie
the plywood together by using Simpson Strong Tie Plated. Uses countersink screw to attach the plates
into the plywood. I would use duct tape to soften the corners of the plates.

Unfortunately if you installed linoleum over those tie
plates, the linoleum will probably be cut by the plate. So, I would use an interlocking product that
you can take with you when you move.

If
you are looking for a more natural wood look there is a product by the Place N’
Go, like the Red Oak 18.5 in. x 18.5 in.
Interlocking Waterproof Vinyl Tile with Built-In underlayment.

The 5/16 in. thick body of Place
N Go tiles includes a built-in, flexible underlayment structure that allows
tiles to be laid directly over uneven and rough subfloors as well as over
old-flooring, including grouted ceramic tiles.

I would like to hear about what
you have decided to do and if possible send pictures.